Transition work
from GCSE to AS level
Mathematics
1
Core Mathematics Transition
Your AS level in mathematics will consist of two Core Mathematics modules and one
Applied Mathematics module.
AS level mathematics uses many of the skills you developed at GCSE. The big
difference is that you will be expected to recognise where you use these skills and
apply them quickly and efficiently.
Your success at AS level Core Mathematics will depend on how willing you are to
maintain and perfect these skills.
In order to get off to a good start you need to be prepared. This booklet will help you
get ready for AS Mathematics. Read through the advice at the start and the end of
the holidays and answer all of the questions to the best of your ability. You will need
to hand in your answers in the first lesson in September.
This work is compulsory for all students.
A set of “MathsWatch” references is provided to help you with this work.
Skills for success
Be organised – keep your notes and work in clearly labelled folders. Make sure you
know where everything is and that you can find it easily.
Make sure your notes are clear and detailed – not everything of use will be written on
the board. Listen carefully to what the teacher says and note down any useful hints
and tips. Your teacher will model the best way to approach problems or apply skills
so you need to make sure your notes clearly show what they were doing. Re-write
out any notes that are scruffy or not clear. Annotate any handouts that you are given.
Read through your notes to check you have everything you need and, if not, talk to
your teacher about what you think is missing.
Be precise with your notation – you will probably have developed some bad
presentation habits at GCSE level. Look at the way the teacher models each
technique and try to do things in the same way. One difference between AS level
and GCSE is that the way things are set out becomes far more important.
Be accurate with your answers – AS level questions often have several joined parts
where one answer feeds into the next. You will need to be accurate so that your
answers make sense. Feeding a wrong answer in to a calculation often results in
something far more difficult to work out. Learn the quick checks that your teacher
uses to test the accuracy of calculations.
2
Plan your time effectively – You will be taught a number of new skills. You will not
become fluent in these unless you practise them. It is not enough to just understand
what the teacher is telling you about a technique, you must practise it to become
confident in it. This is true of all skills based subjects. Make sure you have the time
to do all of the homework set for the deadline you are given.
Be prepared to change the way you do things – GCSE methods are not always the
quickest or most efficient way of doing things. Skills you previously learned for GCSE
often need to be refined. Try not to stubbornly stick to the GCSE way of doing things.
Get help from as many places as possible – it is vitally important that you understand
the work as you go along. Be honest with yourself when you don’t understand
something and seek help. You can get some help from your peers, the text book or
your teacher. The important thing is not to allow a technique or skill to pass by
without understanding it.
Learn these before starting work
Indices
Laws of indices
a0  1
a
1
1

a
m
a n  n am 
a m  a n  a mn
a  b  ab
am
 a m  a n  a mn
n
a
a
a 
1
m n
a2  a
Surds
b

a
b
 a mn
 a
n
m
Quadratic Equations
For ax  bx  c  0
2
 b  b 2  4ac
this is known as the quadratic formula
x
2a
Transition exercises for Core
(Please complete the Core and Statistics work on separate sheets of paper)
1. Collecting like terms:
Simplify the following expressions
a) x 3  2 x 2  5 x  7 x 2  3x  4
b) x 4  3x 3  2 x 2  2 x 3  6 x 2  4 x
c) 2ab  a 2  4b 2  2ab
d) 3x 2  6 xy  12 x  2 xy  6 y 2  8 y
3
2. Indices
Evaluate (i.e. work out)
a) 2 3
b) 25
1
2
1
c)  
3
2
 64 
d)  
 27 

4
3
1
3
 1 2
e)  6 
 4
f) 49 2
3. Laws of Indices
Simplify the following expressions
a) 7 3  7 4
b)
g)  2 p 2 q 3  h)
4
34  36
35
c) 4 3  d)
8
25  29
2 
3 5
e) 4 x 3  2 x 5
f) 3a 
3
2 x 2 y 3 z  6 x 4 yz 3
9 xy z 
4
2 2
4. Changing the subject of a formula
Make the variable shown in brackets the subject
a) v  u  at
b) s 
1
u  v t
2
a 
v
c) A  2r 2  2rh
h 
x 1
x 1
x 
d) y 
5. Expanding brackets
Multiply out and simplify
a) 6( 2 x  3)
b)  2 x( x  5)
5 y (4  3x)  2 x(3  2 y )
c) 2 xy 2 (3x  5 y)
d)
e) ( x  7)( x  7)
g) (2 x  y )( 2  3 y )
h) (3a  4b)(5b  2a)
c) 7 x 2 y  21x 3 y 2
d) 30 xy  6 x 2  15x
f) (2 x  3)( x  5)
6. Factorising expressions
Factorise fully
a) 7 x  21
b) 3ab  12b
4
7. Factorising quadratic expressions
Factorise
a) x 2  9 x  20
b) x 2  12 x  35
c) y 2  2 y  63
d) a 2  6a  16
e) 2 x 2  3x  1
f) 2 x 2  5xy  3 y 2
g) x 2  9
h) 9 x 2  25 y 2
i) 16 x 2  3
8. Solving quadratic equations
Solve the following equations
a) x 2  15 x  54  0
b) t 2  3t  40  0
c) 3x 2  x  14  0
d) 7a  6a 2  20  0
e) 9 x 2  12 x  4  0
f) x  1 
6
x
9. Solving quadratic equations
Solve the following equations giving your answer in surd form
a) x 2  12 x  20  0
b) t 2  9t  4  0
c) 3 x 2  7 x  1
10. Surds
Simplify the following into the form a b ,where b is as small as possible
a)
44
b)
320
c) 75
e)
32
25
f)
27
16
g)
50
9
d)
304
e)
496
304
11. Surds
Write each of the following in its simplest form
a) 4 7  3 7  6 7
d)

7 3

7 3
b) 4 2  50  98

c) 3 7  2 3


12. Solving Simultaneous equations
Solve each of the following pairs of simultaneous equations
a)
3 x  2 y  13
2x  y  2
b)
2 x  3 y  10
5x  2 y  3
c)
3x  y  7
2 x  3 y  23
5
d)
8x  4 y  5
6x  8 y  1
13. Solving Simultaneous equations
Solve each of the following pairs of simultaneous equations
y  x2  x  6
a)
y  x2
b)
y  2x  3
y (5  x)  20
MathsWatch References
The following MathsWatch clips will help you prepare for your AS level course
www.mathswatchvle.com
centre ID is “chippingcampden”
Indices
Clip 156
Factorising
Clips 104 and 140
Algebraic Fractions
Clip 163
Changing the subject
of a formula
Clip 107
Quadratic Equations
Clips 140, 161 and 162
Simultaneous
Equations
Clips 142 and 165
Surds
Clips 157 and 158
6
Transition work for statistics
(Please remember to complete this on separate paper to the Core work)
1.
The following gives the scores of a cricketer in 40 consecutive innings
6
72
14
21
18
85
75
11
27
25
86
36
19
84
37
11
57
43
20
29
12
31
42
34
28
63
8
55
38
0
42
62
45
26
0
16
66
17
33
82
a) Illustrate the data on a stem and leaf diagram.
b) State an advantage that the diagram has over the data.
c) What information is given by the data that does not appear in the diagram?
2.
Certain insects can cause small growths, called ‘galls’, on the leaves of trees.
The numbers of galls found on 60 leaves of an oak tree are given below.
5
16
73
7
18
19
27
14
89
39
21
48
23
1
44
a)
Put the data into a grouped frequency table with classes 0-9, 10-19…,
70-99.
Draw a histogram of the data
Draw a cumulative frequency diagram and use it to estimate the
number of leaves with fewer than 34 galls.
State an assumption required for your estimate in part (c), and briefly
discuss its justification in this case.
b)
c)
d)
4
51
9
2
10
17
69
2
50
33
10
32
0
33
9
0
1
1
22
11
61
25
37
0
51
3
51
31
75
8
31
22
95
7
36
15
28
10
23
44
39
29
24
9
10
3.
The traffic noise levels on two city streets were measured one weekday,
between 5.30am and 8.30pm. There were 92 measurements on each street, made
at equal time intervals, and the results were summarised in the following grouped
frequency table.
Noise
level
dB
Street
1 freq
Street
2 freq
<65
65-67 67-69 69-71 71-73 73-75 75-77 77-79
>79
4
11
18
23
16
9
5
4
2
2
3
7
12
27
16
10
8
7
Compare the noise levels in both streets. Show your working.
7
4.
The number of times each week that a factory machine broke down was
noted over a period of 50 consecutive weeks. The results are given in the following
table.
No of
0
breakdowns
No of
2
weeks
1
2
3
4
5
6
12
14
8
8
4
2
a) Find the mean number of breakdowns in this period. Is this an exact value or
an estimate?
b) Give the mode and the median of the number of breakdowns.
c) Find the interquartile range of the number of breakdowns in a week
5.
The costs, £x, of regional and national phone calls costing over £0.40 made
by a household over a period of three months are as follows.
0.92
0.40
0.40
0.66
0.49
1.12
0.46
0.52
0.94
0.42
0.64
0.76
0.54
0.48
0.48
0.41
0.57
0.85
0.49
0.46
1.66
0.59
0.49
0.40
0.75
0.42
0.50
0.52
0.65
0.42
0.73
a)
State why it is advisable to omit 1.66 from a stem and leaf diagram of
these data.
b)
Draw an ordered stem and leaf diagram, with 1.66 omitted but noted as
HI 1.66 next to the diagram. (HI is short for high)
c)
For the data obtain the median, mean and mode.
d)
Which of the median, mean and mode would be best used to give the
average cost of a phone call costing over £0.40? Give a reason for your
answer.
6.
Find the median, range and interquartile range of each of the following data
sets. Hence draw a box plot for each set of data
a)
7
4
14
9
12
2
19
6
15
b)
7.6
4.8
1.2
6.9
4.8
7.2
8.1
10.3 4.8
6.7
MathsWatch References
Stem and Leaf diagrams
clip 84
Box plots
clip 145
Histograms
clip 175
Cumulative Frequency
clip 144
8